12a
0145
(K12a
0145
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 4 1 8 7 6
Solving Sequence
7,12 4,8
9 3 11 6 1 10 5 2
c
7
c
8
c
3
c
11
c
6
c
12
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−u
95
+ 37u
93
+ ··· + b − u, −u
95
+ u
94
+ ··· + a + 1, u
97
− 2u
96
+ ··· + u − 1i
I
u
2
= hu
7
− 2u
5
+ u
4
+ u
3
− u
2
+ b + u, u
7
+ u
6
− 2u
5
− 2u
4
+ u
3
+ u
2
+ a + u + 1,
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 105 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−u
95
+37u
93
+· · ·+b−u, −u
95
+u
94
+· · ·+a+1, u
97
−2u
96
+· · ·+u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
u
95
− u
94
+ ··· + u − 1
u
95
− 37u
93
+ ··· − u
2
+ u
a
8
=
1
u
2
a
9
=
−u
15
+ 6u
13
− 14u
11
+ 14u
9
− 2u
7
− 6u
5
+ 2u
3
+ 2u
−u
15
+ 5u
13
− 8u
11
+ u
9
+ 8u
7
− 4u
5
− 2u
3
+ u
a
3
=
u
95
− u
94
+ ··· + 5u
3
− u
2
2u
96
− u
95
+ ··· − 8u
2
+ 2
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
1
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
+ u
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
5
=
u
10
− 5u
8
+ 8u
6
− 3u
4
− 3u
2
+ 1
u
12
− 4u
10
+ 4u
8
+ 2u
6
− 3u
4
− 2u
2
a
2
=
u
95
− u
94
+ ··· − 4u
2
+ u
u
96
− 39u
94
+ ··· + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 9u
96
− 8u
95
+ ··· − 13u − 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
97
+ 45u
96
+ ··· + 33u + 1
c
2
, c
4
u
97
− 9u
96
+ ··· − u + 1
c
3
, c
8
u
97
− u
96
+ ··· + 384u + 256
c
5
u
97
− 2u
96
+ ··· + 1189u + 137
c
6
, c
7
, c
11
u
97
+ 2u
96
+ ··· + u + 1
c
9
u
97
+ 8u
96
+ ··· + 1059257u + 154033
c
10
, c
12
u
97
− 6u
96
+ ··· − 239u + 77
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
97
+ 23y
96
+ ··· + 1253y −1
c
2
, c
4
y
97
− 45y
96
+ ··· + 33y −1
c
3
, c
8
y
97
+ 51y
96
+ ··· − 1130496y −65536
c
5
y
97
+ 98y
95
+ ··· − 285079y −18769
c
6
, c
7
, c
11
y
97
− 80y
96
+ ··· + 9y −1
c
9
y
97
+ 36y
96
+ ··· − 192418294111y −23726165089
c
10
, c
12
y
97
+ 64y
96
+ ··· + 69133y −5929
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.076300 + 0.183005I
a = 0.130363 − 0.085867I
b = −0.006250 − 0.958976I
−1.51529 − 2.04174I 0
u = 1.076300 − 0.183005I
a = 0.130363 + 0.085867I
b = −0.006250 + 0.958976I
−1.51529 + 2.04174I 0
u = −1.118950 + 0.358927I
a = 0.204765 − 1.283210I
b = −1.44474 − 2.86226I
2.58320 − 8.29355I 0
u = −1.118950 − 0.358927I
a = 0.204765 + 1.283210I
b = −1.44474 + 2.86226I
2.58320 + 8.29355I 0
u = −0.126507 + 0.813406I
a = −0.88778 − 2.82040I
b = 0.656917 + 0.751120I
5.60707 + 12.55680I −7.94553 − 8.56908I
u = −0.126507 − 0.813406I
a = −0.88778 + 2.82040I
b = 0.656917 − 0.751120I
5.60707 − 12.55680I −7.94553 + 8.56908I
u = −0.114542 + 0.813510I
a = 0.90688 + 2.89676I
b = −0.511057 − 0.767427I
7.79765 + 6.77920I −4.92908 − 4.46483I
u = −0.114542 − 0.813510I
a = 0.90688 − 2.89676I
b = −0.511057 + 0.767427I
7.79765 − 6.77920I −4.92908 + 4.46483I
u = −0.073078 + 0.816109I
a = 0.85010 + 2.82869I
b = −0.042433 − 0.632490I
9.09233 + 2.43008I −3.53506 − 2.81478I
u = −0.073078 − 0.816109I
a = 0.85010 − 2.82869I
b = −0.042433 + 0.632490I
9.09233 − 2.43008I −3.53506 + 2.81478I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.053392 + 0.816761I
a = −0.86603 − 2.65617I
b = −0.104329 + 0.536098I
7.87684 − 3.37088I −5.11230 + 2.63195I
u = −0.053392 − 0.816761I
a = −0.86603 + 2.65617I
b = −0.104329 − 0.536098I
7.87684 + 3.37088I −5.11230 − 2.63195I
u = 0.111101 + 0.799935I
a = 1.288940 + 0.391351I
b = 0.188694 − 0.395318I
2.82430 − 6.28995I −8.96385 + 6.07637I
u = 0.111101 − 0.799935I
a = 1.288940 − 0.391351I
b = 0.188694 + 0.395318I
2.82430 + 6.28995I −8.96385 − 6.07637I
u = −1.137870 + 0.358762I
a = −0.05121 + 1.51386I
b = 1.60910 + 3.09123I
4.67850 − 2.52431I 0
u = −1.137870 − 0.358762I
a = −0.05121 − 1.51386I
b = 1.60910 − 3.09123I
4.67850 + 2.52431I 0
u = 1.144730 + 0.337722I
a = −0.109726 − 0.311521I
b = −0.944110 − 0.801712I
−0.31619 + 2.14672I 0
u = 1.144730 − 0.337722I
a = −0.109726 + 0.311521I
b = −0.944110 + 0.801712I
−0.31619 − 2.14672I 0
u = −0.103420 + 0.790241I
a = −0.96997 − 3.10450I
b = 0.323567 + 1.128250I
1.70977 + 3.78539I −7.61756 − 4.82864I
u = −0.103420 − 0.790241I
a = −0.96997 + 3.10450I
b = 0.323567 − 1.128250I
1.70977 − 3.78539I −7.61756 + 4.82864I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085353 + 0.791661I
a = −1.038950 − 0.762296I
b = −0.252154 + 0.312520I
3.68280 − 1.75925I −7.15174 + 0.63615I
u = 0.085353 − 0.791661I
a = −1.038950 + 0.762296I
b = −0.252154 − 0.312520I
3.68280 + 1.75925I −7.15174 − 0.63615I
u = −1.160010 + 0.325334I
a = 0.19316 − 2.24370I
b = −1.63673 − 3.84153I
−1.49498 + 0.27763I 0
u = −1.160010 − 0.325334I
a = 0.19316 + 2.24370I
b = −1.63673 + 3.84153I
−1.49498 − 0.27763I 0
u = 1.182250 + 0.335072I
a = 0.255858 + 0.190904I
b = 1.180070 + 0.374378I
0.33868 − 2.32547I 0
u = 1.182250 − 0.335072I
a = 0.255858 − 0.190904I
b = 1.180070 − 0.374378I
0.33868 + 2.32547I 0
u = 0.143920 + 0.749716I
a = 0.840542 − 0.473330I
b = −0.143901 − 0.352024I
1.23810 − 1.61799I −7.46158 − 0.93127I
u = 0.143920 − 0.749716I
a = 0.840542 + 0.473330I
b = −0.143901 + 0.352024I
1.23810 + 1.61799I −7.46158 + 0.93127I
u = −1.190710 + 0.363826I
a = 0.53577 + 1.88222I
b = 2.10121 + 3.28700I
5.66672 + 1.82828I 0
u = −1.190710 − 0.363826I
a = 0.53577 − 1.88222I
b = 2.10121 − 3.28700I
5.66672 − 1.82828I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.234940 + 0.251161I
a = 0.0367038 − 0.0468935I
b = 0.429880 − 0.656423I
−1.31278 − 1.68000I 0
u = 1.234940 − 0.251161I
a = 0.0367038 + 0.0468935I
b = 0.429880 + 0.656423I
−1.31278 + 1.68000I 0
u = −1.210910 + 0.365700I
a = −0.69971 − 1.90645I
b = −2.14117 − 3.22189I
4.31801 + 7.63181I 0
u = −1.210910 − 0.365700I
a = −0.69971 + 1.90645I
b = −2.14117 + 3.22189I
4.31801 − 7.63181I 0
u = 0.067904 + 0.716739I
a = 0.005795 − 1.052530I
b = −0.418357 + 0.045210I
2.22161 − 1.81122I −6.58757 + 4.34433I
u = 0.067904 − 0.716739I
a = 0.005795 + 1.052530I
b = −0.418357 − 0.045210I
2.22161 + 1.81122I −6.58757 − 4.34433I
u = 0.694155 + 0.155276I
a = −0.129694 − 0.373429I
b = −0.284181 + 0.715904I
−1.64822 + 1.85592I −13.39585 − 2.90468I
u = 0.694155 − 0.155276I
a = −0.129694 + 0.373429I
b = −0.284181 − 0.715904I
−1.64822 − 1.85592I −13.39585 + 2.90468I
u = 0.166510 + 0.680908I
a = −0.652095 + 1.069380I
b = 0.462505 + 0.336470I
0.37978 − 5.08479I −10.13756 + 7.85339I
u = 0.166510 − 0.680908I
a = −0.652095 − 1.069380I
b = 0.462505 − 0.336470I
0.37978 + 5.08479I −10.13756 − 7.85339I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.290550 + 0.155428I
a = 0.330614 + 0.169609I
b = 0.634930 − 0.619092I
−1.26131 − 1.89849I 0
u = 1.290550 − 0.155428I
a = 0.330614 − 0.169609I
b = 0.634930 + 0.619092I
−1.26131 + 1.89849I 0
u = −1.299620 + 0.260517I
a = 1.71939 + 0.85305I
b = 2.59874 + 0.76974I
−4.80583 + 2.13843I 0
u = −1.299620 − 0.260517I
a = 1.71939 − 0.85305I
b = 2.59874 − 0.76974I
−4.80583 − 2.13843I 0
u = −1.335730 + 0.026914I
a = 1.229910 + 0.335097I
b = 1.44608 + 0.35864I
−5.57709 + 0.21725I 0
u = −1.335730 − 0.026914I
a = 1.229910 − 0.335097I
b = 1.44608 − 0.35864I
−5.57709 − 0.21725I 0
u = 1.310410 + 0.279225I
a = 0.688209 + 0.224075I
b = 0.37451 + 1.55998I
−5.06350 − 4.46571I 0
u = 1.310410 − 0.279225I
a = 0.688209 − 0.224075I
b = 0.37451 − 1.55998I
−5.06350 + 4.46571I 0
u = −0.535358 + 0.374511I
a = 1.62509 + 1.47845I
b = 0.223110 + 0.775600I
1.26298 + 8.74212I −11.9170 − 9.0216I
u = −0.535358 − 0.374511I
a = 1.62509 − 1.47845I
b = 0.223110 − 0.775600I
1.26298 − 8.74212I −11.9170 + 9.0216I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.312070 + 0.304653I
a = −0.978270 − 0.798937I
b = −1.60919 − 0.98606I
−2.10580 + 5.52005I 0
u = −1.312070 − 0.304653I
a = −0.978270 + 0.798937I
b = −1.60919 + 0.98606I
−2.10580 − 5.52005I 0
u = 1.301650 + 0.360247I
a = 1.24554 − 0.95339I
b = 3.26147 − 1.62863I
3.64680 − 0.86350I 0
u = 1.301650 − 0.360247I
a = 1.24554 + 0.95339I
b = 3.26147 + 1.62863I
3.64680 + 0.86350I 0
u = 1.333670 + 0.214386I
a = 0.091767 − 0.625950I
b = −0.0419970 + 0.0777167I
−2.98555 + 2.91120I 0
u = 1.333670 − 0.214386I
a = 0.091767 + 0.625950I
b = −0.0419970 − 0.0777167I
−2.98555 − 2.91120I 0
u = −0.040986 + 0.644398I
a = −0.470789 + 1.316680I
b = 0.877565 + 0.056288I
−0.789349 + 1.067810I −12.54494 − 0.17404I
u = −0.040986 − 0.644398I
a = −0.470789 − 1.316680I
b = 0.877565 − 0.056288I
−0.789349 − 1.067810I −12.54494 + 0.17404I
u = 1.361170 + 0.045050I
a = −1.68001 + 0.84178I
b = −2.82631 + 2.17159I
−7.87318 − 1.71980I 0
u = 1.361170 − 0.045050I
a = −1.68001 − 0.84178I
b = −2.82631 − 2.17159I
−7.87318 + 1.71980I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.315640 + 0.358977I
a = −1.47555 + 1.24858I
b = −3.69497 + 1.94814I
4.74652 − 6.65977I 0
u = 1.315640 − 0.358977I
a = −1.47555 − 1.24858I
b = −3.69497 − 1.94814I
4.74652 + 6.65977I 0
u = −1.323330 + 0.342677I
a = −0.124269 − 1.289700I
b = −0.37275 − 1.97282I
−0.73515 + 5.85059I 0
u = −1.323330 − 0.342677I
a = −0.124269 + 1.289700I
b = −0.37275 + 1.97282I
−0.73515 − 5.85059I 0
u = −1.368030 + 0.059939I
a = −1.29273 − 0.90938I
b = −1.60119 − 1.03501I
−7.09539 + 4.13757I 0
u = −1.368030 − 0.059939I
a = −1.29273 + 0.90938I
b = −1.60119 + 1.03501I
−7.09539 − 4.13757I 0
u = 1.374290 + 0.079537I
a = 1.62166 + 0.00987I
b = 2.59757 − 0.79140I
−2.53211 − 4.62583I 0
u = 1.374290 − 0.079537I
a = 1.62166 − 0.00987I
b = 2.59757 + 0.79140I
−2.53211 + 4.62583I 0
u = 1.333520 + 0.341806I
a = 1.77954 − 2.08217I
b = 4.58642 − 2.78774I
−2.80433 − 7.87203I 0
u = 1.333520 − 0.341806I
a = 1.77954 + 2.08217I
b = 4.58642 + 2.78774I
−2.80433 + 7.87203I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.348380 + 0.289480I
a = 1.44252 + 0.02874I
b = 2.06872 − 0.16790I
−4.37828 + 8.63452I 0
u = −1.348380 − 0.289480I
a = 1.44252 − 0.02874I
b = 2.06872 + 0.16790I
−4.37828 − 8.63452I 0
u = −1.338200 + 0.346591I
a = −0.258393 + 1.359040I
b = −0.24512 + 2.10842I
−1.73047 + 10.42640I 0
u = −1.338200 − 0.346591I
a = −0.258393 − 1.359040I
b = −0.24512 − 2.10842I
−1.73047 − 10.42640I 0
u = −0.484186 + 0.378282I
a = −1.50954 − 1.53900I
b = −0.322758 − 0.792431I
3.24484 + 3.24235I −8.65530 − 4.94862I
u = −0.484186 − 0.378282I
a = −1.50954 + 1.53900I
b = −0.322758 + 0.792431I
3.24484 − 3.24235I −8.65530 + 4.94862I
u = −1.349460 + 0.319480I
a = −0.829122 + 0.586131I
b = −1.15265 + 0.96709I
−3.46530 + 5.49686I 0
u = −1.349460 − 0.319480I
a = −0.829122 − 0.586131I
b = −1.15265 − 0.96709I
−3.46530 − 5.49686I 0
u = 1.341310 + 0.353804I
a = −2.06581 + 1.68918I
b = −4.57878 + 2.14247I
3.22187 − 10.98640I 0
u = 1.341310 − 0.353804I
a = −2.06581 − 1.68918I
b = −4.57878 − 2.14247I
3.22187 + 10.98640I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.390800 + 0.073948I
a = −1.94759 − 0.11301I
b = −3.08499 + 0.56757I
−4.75509 − 10.05740I 0
u = 1.390800 − 0.073948I
a = −1.94759 + 0.11301I
b = −3.08499 − 0.56757I
−4.75509 + 10.05740I 0
u = 1.348030 + 0.352429I
a = 2.21445 − 1.72567I
b = 4.71204 − 2.06495I
0.9676 − 16.7600I 0
u = 1.348030 − 0.352429I
a = 2.21445 + 1.72567I
b = 4.71204 + 2.06495I
0.9676 + 16.7600I 0
u = −1.395620 + 0.017256I
a = −0.419590 − 1.142350I
b = −0.52309 − 1.38433I
−7.89376 − 1.50579I 0
u = −1.395620 − 0.017256I
a = −0.419590 + 1.142350I
b = −0.52309 + 1.38433I
−7.89376 + 1.50579I 0
u = −0.303128 + 0.514916I
a = 0.760246 + 1.014040I
b = 0.734346 + 0.775395I
1.99642 − 5.50453I −9.70697 + 2.05579I
u = −0.303128 − 0.514916I
a = 0.760246 − 1.014040I
b = 0.734346 − 0.775395I
1.99642 + 5.50453I −9.70697 − 2.05579I
u = −0.338950 + 0.455365I
a = −0.93268 − 1.30856I
b = −0.595427 − 0.780173I
3.69304 − 0.15503I −6.96002 − 3.29097I
u = −0.338950 − 0.455365I
a = −0.93268 + 1.30856I
b = −0.595427 + 0.780173I
3.69304 + 0.15503I −6.96002 + 3.29097I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.467931 + 0.308565I
a = 0.084687 − 0.878435I
b = −0.670638 + 0.271758I
−1.42451 − 3.05583I −14.0334 + 7.0667I
u = 0.467931 − 0.308565I
a = 0.084687 + 0.878435I
b = −0.670638 − 0.271758I
−1.42451 + 3.05583I −14.0334 − 7.0667I
u = −0.430554 + 0.233040I
a = 1.65460 + 2.24861I
b = 0.407916 + 0.668554I
−2.34524 + 0.90469I −12.7209 − 7.5741I
u = −0.430554 − 0.233040I
a = 1.65460 − 2.24861I
b = 0.407916 − 0.668554I
−2.34524 − 0.90469I −12.7209 + 7.5741I
u = 0.248050 + 0.339715I
a = −0.509169 + 1.177470I
b = 0.609743 + 0.066227I
−0.830925 + 0.497747I −11.61503 + 1.83140I
u = 0.248050 − 0.339715I
a = −0.509169 − 1.177470I
b = 0.609743 − 0.066227I
−0.830925 − 0.497747I −11.61503 − 1.83140I
u = 0.337597
a = −0.676853
b = 0.328344
−0.597166 −16.5590
14
II. I
u
2
= hu
7
− 2u
5
+ u
4
+ u
3
− u
2
+ b + u, u
7
+ u
6
− 2u
5
− 2u
4
+ u
3
+ u
2
+
a + u + 1, u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
4
=
−u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− u
2
− u − 1
−u
7
+ 2u
5
− u
4
− u
3
+ u
2
− u
a
8
=
1
u
2
a
9
=
1
u
2
a
3
=
−u
7
− u
6
+ 2u
5
+ 2u
4
− u
3
− u
2
− u − 1
−u
7
+ 2u
5
− u
4
− u
3
+ u
2
− u
a
11
=
u
u
a
6
=
−u
2
+ 1
−u
2
a
1
=
−u
5
+ 2u
3
− u
−u
5
+ u
3
+ u
a
10
=
−u
3
+ 2u
−u
5
+ u
3
+ u
a
5
=
u
5
− 2u
3
+ u
u
5
− u
3
− u
a
2
=
−u
7
− u
6
+ u
5
+ 2u
4
+ u
3
− u
2
− 2u − 1
−u
7
+ u
5
− u
4
+ u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
7
− 2u
6
− 2u
5
+ 8u
4
− 3u
3
− 7u
2
+ 8u − 19
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
, c
8
u
8
c
4
(u + 1)
8
c
5
, c
9
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
6
, c
7
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
10
, c
12
u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1
c
11
u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
8
c
3
, c
8
y
8
c
5
, c
9
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
6
, c
7
, c
11
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
10
, c
12
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.180120 + 0.268597I
a = −0.663977 − 0.849844I
b = −0.33804 − 1.54318I
−2.68559 − 1.13123I −15.9046 + 0.8051I
u = 1.180120 − 0.268597I
a = −0.663977 + 0.849844I
b = −0.33804 + 1.54318I
−2.68559 + 1.13123I −15.9046 − 0.8051I
u = 0.108090 + 0.747508I
a = 0.727959 − 0.566792I
b = −0.306664 + 0.427719I
0.51448 − 2.57849I −11.78039 + 3.88175I
u = 0.108090 − 0.747508I
a = 0.727959 + 0.566792I
b = −0.306664 − 0.427719I
0.51448 + 2.57849I −11.78039 − 3.88175I
u = −1.37100
a = 0.910598
b = 1.71160
−8.14766 −19.8290
u = −1.334530 + 0.318930I
a = −0.690511 − 0.438656I
b = −1.53294 − 0.14882I
−4.02461 + 6.44354I −16.5091 − 6.0410I
u = −1.334530 − 0.318930I
a = −0.690511 + 0.438656I
b = −1.53294 + 0.14882I
−4.02461 − 6.44354I −16.5091 + 6.0410I
u = 0.463640
a = −1.65754
b = −0.356309
−2.48997 −16.7830
18
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
97
+ 45u
96
+ ··· + 33u + 1)
c
2
((u − 1)
8
)(u
97
− 9u
96
+ ··· − u + 1)
c
3
, c
8
u
8
(u
97
− u
96
+ ··· + 384u + 256)
c
4
((u + 1)
8
)(u
97
− 9u
96
+ ··· − u + 1)
c
5
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
97
− 2u
96
+ ··· + 1189u + 137)
c
6
, c
7
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)(u
97
+ 2u
96
+ ··· + u + 1)
c
9
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
· (u
97
+ 8u
96
+ ··· + 1059257u + 154033)
c
10
, c
12
(u
8
+ 3u
7
+ 7u
6
+ 10u
5
+ 11u
4
+ 10u
3
+ 6u
2
+ 4u + 1)
· (u
97
− 6u
96
+ ··· − 239u + 77)
c
11
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)(u
97
+ 2u
96
+ ··· + u + 1)
19
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
8
)(y
97
+ 23y
96
+ ··· + 1253y −1)
c
2
, c
4
((y −1)
8
)(y
97
− 45y
96
+ ··· + 33y −1)
c
3
, c
8
y
8
(y
97
+ 51y
96
+ ··· − 1130496y −65536)
c
5
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
97
+ 98y
95
+ ··· − 285079y −18769)
c
6
, c
7
, c
11
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· (y
97
− 80y
96
+ ··· + 9y −1)
c
9
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
· (y
97
+ 36y
96
+ ··· − 192418294111y −23726165089)
c
10
, c
12
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
· (y
97
+ 64y
96
+ ··· + 69133y −5929)
20
